The synchronicity
assumption made by classical reactive synthesis is motivated by the
fact that such methods focus on the control of systems rather than on
the data, in the sense that input symbols are Boolean signals issued
by some environment, and output symbols are actions controlling the
system in order to fulfil some correctness properties. From a
data-processing perpective, this is a strong limitation. The
synthesis of systems which need to process streams of data, like a monitoring system or a
system which cleans noisy data coming from sensors, cannot be
addressed using classical \(\omega \) -regular synthesis. Therefore, one
needs to extend specifications to asynchronous specifications, in the
sense that the specifications must describe properties of executions
which do not strictly alternate between inputs and outputs. Already on
finite words however, the synthesis problem of asynchronous
specifications by asynchronous implementations, both defined by
transducers, is undecidable in general [1]}, and
decidable only in some restricted cases [2]}.
The second limitation \((ii)\)  is addressed in the next paragraph.
